Why does Juliet bid Romeo to "swear not by the moon"?
This quote comes from Act II, Scene II or Romeo and Juliet, often referred to as "the balcony scene." Here, Romeo has come wandering on the Capulet's property when he spies Juliet at her window above. She speaks to herself about how she wishes Romeo was not a Montague, when he yells up to her that he feels the same. Juliet professes her love for Romeo, despite who he is, and says that if Romeo swears he loves her, she will believe him. Romeo swears that by "yonder blessed moon" he loves her- meaning his love for her is as real as the moon, or that if he were to lie to her the moon would suffer damage or disappear. Juliet pleads with him not to swear by the moon because it is inconsistent and changes within a month.
Juliet is asking Romeo not to swear by the moon because the moon appears different every day, and she does not want his love to be the same. She wants a true and lasting love, not something that will wane quickly or only feel like love some of the time. Love and the prospect of marriage were highly contractual in Renaissance Italy, so Juliet is safeguarding her love by asking Romeo not to swear by the moon. Imagine how different this play would have been if Romeo were to change his mind about Juliet and say that he no longer was obligated to love Juliet because the moon had changed its phase!